Show the Proof¶

In [1]:

import proveit
# Automation is not needed when only showing a stored proof:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%show_proof

Out[1]:

	step type	requirements	statement
0	instantiation	1, 2, 3	⊢
	: , : , :
1	reference	12	⊢
2	instantiation	4, 5	⊢
	: , : , :
3	instantiation	12, 6, 7	⊢
	: , : , :
4	axiom		⊢
	proveit.logic.equality.substitution
5	instantiation	8, 9	⊢
	:
6	instantiation	10, 46, 20, 19, 11, 21, 23, 24	⊢
	: , : , : , : , : , :
7	instantiation	12, 13, 14	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
9	instantiation	15, 16	⊢
	:
10	theorem		⊢
	proveit.numbers.addition.disassociation
11	instantiation	28	⊢
	: , :
12	axiom		⊢
	proveit.logic.equality.equals_transitivity
13	instantiation	17, 46, 19, 21, 23, 24	⊢
	: , : , : , : , : , : , :
14	instantiation	18, 19, 20, 46, 21, 22, 23, 24, 25^*	⊢
	: , : , : , : , : , :
15	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonneg_if_in_real_nonneg
16	instantiation	44, 26, 27	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.addition.leftward_commutation
18	theorem		⊢
	proveit.numbers.addition.association
19	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
20	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
21	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
22	instantiation	28	⊢
	: , :
23	instantiation	44, 30, 29	⊢
	: , : , :
24	instantiation	44, 30, 31	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
26	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonneg
27	instantiation	32, 37, 33	⊢
	: , :
28	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
29	instantiation	44, 34, 35	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
31	instantiation	44, 36, 37	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.addition.add_real_pos_closure_bin
33	instantiation	44, 38, 39	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
35	instantiation	44, 40, 41	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
37	assumption		⊢
38	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
39	instantiation	44, 42, 43	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
41	instantiation	44, 45, 46	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
43	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
44	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
45	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
46	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements